Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C5×#124 | C2 | semidirect |
| 2. C2×#689 | C2 | semidirect |
| 3. C2×#688 | C2 | semidirect |
| 4. C2×#687 | C2 | semidirect |
| 6. #4021 | C2 | semidirect |
| 7. C4×#168 | C2 | semidirect |
| 43. #124 | D5 | semidirect |
| 88. C5 | #495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#124 | 2 |
| C2×#689 | 2 |
| C2×#688 | 2 |
| C2×#687 | 2 |
| C2×#686 | 2 |
| #4021 | 2 |
| C4×#168 | 2 |
| #495 | 5 |